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I am not sure what you mean by "hidden attractions" and by "outside the Paris city".

The City of Paris is quite small, but it is surrounded by a vast ring of banlieues which have not many attractions at all.

Out of this ring, you find some splendid castles (besides Versailles: Fontainebleau and Chantilly) and picturesque historic towns like Rouen or Auxerre (easy to reach by train). Even the Loire castles are just one hour train ride from Gare Montparnasse.

For more special attractions (like unusual museums or minor archeological sites in the woods), consult a good guidebook like the Michelin Green Guide Paris Île de France.

Scattered around the heart of the right bank, are the 19th century shopping arcades, the passages & galleries, great fun to wander through. I supposed they'd be well known but after spending time visiting them during the past week I saw few other tourists and had a wonderful time. Google "paris passages" for more information and locations.

Any of the smaller museums will be less crowded than the big ones that are so popular (Louvre, Orsay, Orangerie and Picasso now, most likely). There are tons of museums in Paris. I quite like the PEtit Palais which has many periods and is free, to boot. So if you don't have any particular museum you really want to see especially, go to the city of Paris-run ones which are free. I suppose the Rodin is fairly busy now that I think of it, even though small (not free, though). But even the Maillol, which I really like, can get busy, as well as the Cluny.

So I think you have to narrow down what type of museum and/or art you wish to see. I love the Invalides which is a military history museum, for example. It isn't free nor small, but I've never felt it crowded -- nothing like the Louvre or Orsay.

I enjoyed the Postal Museum, also, and believe me, it isn't crowded. Really liked the Nissim Camondo house, also, and it has never been that crowded when I was there. But there is only so much time in the day.

Parks in the outer areas aren't that crowded, like Montsouris. I could go on and on, but I do agree that if you haven't been there, you probably would most like to see some of the most famous sites, that is normal (like Notre Dame, etc) and why go only to go to second-rate sites because they aren't crowded.

So maybe think about what your interests are and then plan around those. OUtside Paris, the famous chateaux are fairly crowded (like Chantilly, not to mention Versailles which can be packed). But Empress Josephine's house wasn't that crowded and was interesting (Malmaison) http://musees-nationaux-malmaison.fr/chateau-malmaison/

Auvers-sur-Oise, Van Gogh's last residence, is a very interesting little town just outside Paris and sure, a few of the main sites were crowded (like his home) but not oppressively so, and the town at large didn't feel crowded to me.

Some of those places like Malmaison and Auvers require a bit more planning and research for you to understand the logistics, though.

I have an idea -- the chateau de Vincennes at the end of the metro line on the east is easy to get to and it isn't really that crowded, very important historically. http://www.chateau-de-vincennes.fr/en/

Montmartre is pretty crowded in any area where tourists go, generally around Sacre Coeur.

The rose gardens in Bois de Boulogne are beautiful and not really that crowded compared to any main gardens right in Paris. Again, a bit more trouble to get to.